Lawn reinforcement/protection mesh

I'm thinking of using some lawn protection mesh once I've managed to level it as best I can. Has anybody used it and is it any good? I don't want it to be very obvious once the grass has grown through it, so would appreciate advice off anyone who's used something similar.

Reason for use is that I have three lovely dogs who usually make mincemeat out of my lawn

 

I have seen it used on parking areas and heavy traffic areas on golf courses . Never seen it used on a house lawn as mutt protection. I have 4 big holes in my back lawn , courtesy of Molly. All attempts to secretly fill them in have failed as she digs them back up !